The present invention is directed to the field of digital telecommunications, particularly systems that employ complex channel modulation techniques. In signal transmission, digital data is typically modulated onto an analog carrier, such as with M-PSK (M-ary Phase Shift Keying) or QAM (Quadrature Amplitude Modulation). In such schemes, it is typical to modulate data into two non-interfering orthogonal signal paths, I and Q (In-phase and Quadrature).
By way of example, a Binary Phase Shift Keying (BPSK) scheme is depicted in FIGS. 1A-1D. During reception of the signal, as shown in FIG. 1A, the analog subcarrier signal is demodulated at the receiver into digital data by taking samples 10 at predetermined intervals. If a positive voltage is detected, a digital value of “1” is indicated. A negative voltage indicates a digital value of “0.” The samples 10 are taken at predetermined intervals at which time a sample decision is made, derived from a clock reference, which is either provided by a local reference within the receiver or is obtained from a clock synchronizer using the demodulated signal itself. The clock reference is presumed accurate so as to not degrade the error performance of the receiver.
The I and Q amplitude axes can be plotted so as to define a complex plane. As is commonly understood in digital communications, a pair of simultaneous I and Q samples define a “symbol.” In a BPSK system, as shown in FIG. 1D, each symbol that can be mapped to the complex plane as one of the digital set {0,1}. But as depicted in FIG. 1C, a time-varying stream of symbols is continuously modulated onto the I and Q subcarriers. Thus, a time-summation of symbols can be seen as a “constellation” 14 in the complex plane, as shown in FIG. 1D.
In a typical digital communications receiver, the decision is made in a decision circuit (typically called a Symbol Detector or Slicer) that reduces one complex symbol of a demodulated waveform into a digital number. In a soft decision receiver this decision may alternatively be in the form of an analog, or multi-bit digital word, representation of the position of the symbol decision on the complex plane (which is subsequently used by a decoding process to obtain the corresponding digital number). In any case, the process of correctly deciding how a given symbol maps into a digital number directly affects the error rate and hence the overall performance of the communication system—the better the symbol map decision, the lower the error rate.
Due to noise in the analog carrier signal, the symbols can vary in amplitude in such a way that the constellations 14 are distributed within the complex plane. Thus, the decision circuit effectively establishes a decision boundary 14 in the complex plane to distinguish between symbols representing a digital “1” and a “0.” Factors such as noise and distortion can create difficulties in establishing a decision boundary, thereby increasing the signal's bit-error rate (BER). As shown in FIGS. 2A and 2B, noise on either the I or Q channels can make the constellations 14 more diffuse so that the decision boundary is unclear. As shown in FIGS. 2C and 2D, in BPSK a DC (Direct Current) offset will shift the decision boundary to favor one or the other symbol. But considering the effects of noise and filtering, the slicer is effectively “off-center,” and some symbols will be incorrectly assigned to the wrong side of the decision boundary, resulting in an excessive increase in the bit-error rate.
In a typical system, a symbol decision circuit maps the symbols into digital numbers on a one-to-one basis. As shown above, in a BPSK (Bi-Phase Shift Keying) system, the two complex half-planes are mapped to the set {0,1}. In higher order schemes, such as QPSK (Quadrature Phase Shift Keying) and QAM (Quadrature Amplitude Modulation), the problems with noise and distortion are increased. As shown in FIGS. 3A, 3B and 3C, with QPSK, both the I and Q channel carry a single-bit signal, so that the symbols in each constellation 14 fall within one of four quadrants in the complex plane, and are mapped to {00,01,11,10}. In QAM, such as a 16QAM scheme as shown in FIGS. 4A, 4B and 4C, the amplitude of the analog signal is varied between two states (i.e. 1V and 3V) so that both I and Q channel carry a two-bit signal. Each of the resulting symbols is represented by four bits (e.g. {0000, 0001, . . . }), resulting in sixteen constellation points being mapped to the complex plane. This process is similar for the large variety of constellations of M-PSK (M-ary Phase Shift Keying) and QAM (Quadrature Amplitude Modulation).
Since the symbol map is essentially fixed by the analog signal amplitude, the decision process can fall prey to mapping distortions in the modulation and demodulation process, resulting in decision errors. Higher order PSK and QAM modulations become extremely sensitive to noise and distortion since the relative symbol separations become less and less as the number of symbols in the modulation set grows. For example, in 64QAM systems, the decision boundaries between constellations can be quite close, thus making them prone to a high BER in the event of noise and distortion.
Several types of distortion are shown in FIGS. 5A, 5B, 5C, 5D, 5E, and 5F. As shown in FIG. 5A, phase errors can produce phase rotation in the map. FIG. 5B shows dilation or I-Q unbalance. FIG. 5C shows the effects of translation or DC offset as indicated in the earlier BPSK example. FIG. 5D shows S-curve distortion resulting from a traveling wave tube or similar device. FIGS. 5E and 5F respectively show “pincushion” and “barrel” distortion. Other types of distortion include “skew” or “leaning,” AM-to-PM distortion from amplitude-induced phase modulation, and AM-to-AM or trapezoidal distortion from non-linear signal amplification, resulting in unequal amplitude gain in one dimension. In a real scenario, mapping errors may result from any combination of these types of distortion.
Some techniques are known for correcting map distortion. Typically, much care is taken in the modulation, demodulation, filtering, and AGC (Automatic Gain Control) processes of the transmit/receive chain in order to minimize these distortions in the first place. Separate AGC functions may be included in the receiver after demodulation (on the in-phase (I) and quadrature (Q) channels) to minimize DC offset and I-Q unbalance. Some communications systems actually measure symbol distortion in the receiver and transmit those measurements back to the transmitter, where “pre-distortion” is used in an attempt to minimize the net system distortion. Tight phase control of the carrier recovery process also aids in minimizing phase rotation.
However, there are many practical scenarios in which there is no available a priori information about potential sources of signal distortion. Therefore, in a practical system that must receive digital modulations from a variety of transmitters in unknown states of age, power regulation, nonlinear amplification, and so forth, symbol decision mapping will inevitably exhibit errors induced by symbol map distortions. Thus, the existing techniques cannot adequately correct map distortion, resulting in unsatisfactory bit-error rates.